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Elliptic singularity

Type of surface singularity used in algebraic geometry

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Source updated November 4, 2024

In algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic genus of its local ring is 1.

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This article is adapted from the Wikipedia article “Elliptic singularity”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Rational singularity

In mathematics, more particularly in the field of algebraic geometry, a scheme X {\displaystyle X} has rational singularities, if it is normal, of finite type over a field of characteristic zero, and there exists a proper birational map f : Y → X {\displaystyle f\colon Y\rightarrow X} from a regular scheme Y {\displaystyle Y} such that the higher direct images of f ∗ {\displaystyle f_{*}} applied to O Y {\displaystyle {\mathcal {O}}_{Y}} are trivial. That is, R i f ∗ O Y = 0 {\displaystyle R^{i}f_{*}{\mathcal {O}}_{Y}=0} for i > 0 {\displaystyle i>0} .